Đáp án:
$\dfrac{\sqrt{uv}}{\sqrt v-\sqrt u}$
Giải thích các bước giải:
ĐKXĐ: $u\ge 0;v\ge 0;u\ne v$
$\dfrac{u-v}{\sqrt u+\sqrt v}-\dfrac{\sqrt u^3+\sqrt v^3}{u-v}$
$=\dfrac{(\sqrt u-\sqrt v)(\sqrt u+\sqrt v)}{\sqrt u+\sqrt v}-\dfrac{(\sqrt u+\sqrt v)(u-\sqrt u.\sqrt v+v)}{(\sqrt u-\sqrt v)(\sqrt u+\sqrt v)}$
$=\sqrt u-\sqrt v-\dfrac{u-\sqrt u.\sqrt v+v}{\sqrt u-\sqrt v}$
$=\dfrac{(\sqrt u-\sqrt v)^2}{\sqrt u-\sqrt v}-\dfrac{u-\sqrt u.\sqrt v+v}{\sqrt u-\sqrt v}$
$=\dfrac{u-2\sqrt u.\sqrt v+v-u+\sqrt u.\sqrt v-v}{\sqrt u-\sqrt v}$
$=\dfrac{\sqrt{uv}}{\sqrt v-\sqrt u}$
